Approximation constant-Q reverse time migration in the time domain: Unsplit-field PML formulation
Ali Fathalian, Kristopher A. H. Innanen
We investigate the simulation of wave propagation in attenuation medium within approximating constant-Q. Such wave propagation can be modelled with a ﬁnite difference scheme by introducing a series of standard linear solid (SLS) mechanisms, and it can be carried out within a computationally tractable region by making use of perfectly-matched layer (PML) boundary conditions. To consider the effects of the number of relaxation mechanisms (L), we compare numerical and analytical solution of the wave equation for a homogeneous and complex medium. In the weak attenuation (Q = 100), the numerical solutions using a series of SLS relaxation mechanisms and analytical solutions agree very well,and the acoustic and viscoacoustic RTM images have similar artifacts and amplitudes in the shallow layers. At the deeper layers, we can see that a series of SLS mechanisms RTM yield comparable results with the acoustic RTM case. In strong attenuation(Q = 20), when the wave reaches greater depth, the error of numerical solutions using single SLS mechanism increase and the viscoacoustic RTM images using a single SLS mechanisms are not so accurate in the deeper layers. Although the results of single SLS relaxation mechanism are still useful for practical application, the three SLS relaxation mechanisms are quite accurate for both weak and strong attenuation.